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Course: STAT 30100
Title: Mathematical Statistics 1
Instructor(s): Mary Sara McPeek
Teaching Assistant(s): Yongrui (Richard) Chen
Class Schedule: Sec 01: TR 1:30–2:50PM in Jones 226
Office Hours:  
Course Homepage: Course Home Page
Textbook(s): Casella, Berger, Statistical Inference, 2nd edition.
Ferguson, Course in Large Sample Theory, 1st edition.
Description: This course is part of a two-quarter sequence on the theory of statistics. Topics will include exponential, curved exponential, and location-scale families; mixtures, hierarchical and conditional modeling including compatibility of conditional distributions; multivariate normal and joint distributions of quadratic forms of multivariate normal; principles of estimation; identifiability, sufficiency, minimal sufficiency, ancillarity, completeness; properties of the likelihood function and likelihood-based inference, both univariate and multivariate, including examples in which the usual regularity conditions do not hold; multivariate information inequality. Part of the course will be devoted to elementary asymptotic methods that are useful in the practice of statistics, including methods to derive asymptotic distributions of various estimators and test statistics, such as Pearson's chi-square, standard and nonstandard asymptotics of maximum likelihood estimators, asymptotics of order statistics and extreme order statistics, Cramer’s theorem including situations in which the second-order term is needed, asymptotic efficiency. Other topics (e.g., methods for dependent observations) may be covered if time permits.

Prerequisite(s): STAT 30400 or consent of instructor